Cyanine dye (S120) aggregated into a specific state, a J-aggregate, in monolayer assemblies was irradiated with gamma-rays at room temperature and the structural changes induced thereby were investigated. We prepared samples with control of the fractions of the J-aggregates in a texture through the Langmuir-Blodgett method. Changes in the assembly structure on irradiation were analyzed by absorption spectra by separately estimating the concentration of the J-aggregates and the "non-J" part, which practically consists of monomers. As a result, it became apparent that the efficiency of dissociation of S120 was highly influenced by differences in the molecular ordering structure. We proposed a model describing the radiation-induced changes in the molecular concentrations in the J-aggregates and the non-J to explain the experimental data.